I'm trying to put down my own house, but I have a little problem. I put my house in the vicinity of Whiterun, and I put some rocks and cliffs around it, but I can't solve this problem. How do you remove some of that brown grasses?

I would love to post a link/picture but I can't for some reason?

The grass is part of the land texture. Press "H" and paint a texture without grass.

You can also press "I" in the render window while the landscape editor is open to see what textures are used in the current cell.
This menu is very useful to replace a texture in the whole cell at once, and to see how many textures are currently used (max 6 per quad)

To see what ground texture is currently used at a certain spot Ctrl+right click on it and the texture will be selected in the Landscape Editor.

If you're referring to grass staying there in the CS when ground is moved and things, it seems to just stay there forever even if it's not there in game.

Ok, but I can only raise or lower the groundtexture, the grass isn't removed. How do I paint a new texture on it?

There's a "paint" checkbox in the land editing window above the lsit of textures. Select that, and to paint them, use right click instead of left click.

Aaahh, RIGHTCLICK instead of leftclick! Thank you!

Even as I paint, the grass won't go away. I just paint the underground.

If I lower the ground, they are floating in the air.

As Dragonbone already mentioned, it will always show up in the CK, even when done properly, but it should have the grass removed when ingame. Have you tried out how it looks when you actually playtest it?

Ok, I will try it.

-edit-

It worked. Thanks!